flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139

/*
    Copyright (C) 2023 Fredrik Johansson

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "gr_vec.h"
#include "gr_poly.h"

int
_gr_poly_sqrt_series_newton(gr_ptr g,
    gr_srcptr h, slong hlen, slong len, slong cutoff, gr_ctx_t ctx)
{
    slong sz = ctx->sizeof_elem;
    int status = GR_SUCCESS;
    slong a[FLINT_BITS];
    slong i, m, n, alloc;
    gr_ptr t, u, v;
    slong tlen, ulen;

    hlen = FLINT_MIN(hlen, len);

    if (len == 0)
        return GR_SUCCESS;

    if (len < cutoff || len == 1)
        return _gr_poly_sqrt_series_basecase(g, h, hlen, len, ctx);

    cutoff = FLINT_MAX(cutoff, 2);
    a[i = 0] = n = len;
    while (n >= cutoff)
        a[++i] = (n = (n + 1) / 2);

    status |= _gr_poly_rsqrt_series_basecase(g, h, FLINT_MIN(hlen, n), n, ctx);

    if (status != GR_SUCCESS)
        return status;

    /* Hack: until all rings have a good mulmid, implement both with and without. */
    /* Todo: tighten allocations when we have mulmid */
    int have_mulmid = (ctx->methods[GR_METHOD_POLY_MULMID] != (gr_funcptr) _gr_poly_mulmid_generic);

    alloc = 2 * len + (len + 1) / 2;

    GR_TMP_INIT_VEC(t, alloc, ctx);
    u = GR_ENTRY(t, len, sz);
    v = GR_ENTRY(u, len, sz);

    for (i--; i >= 1; i--)
    {
        m = n;
        n = a[i];

        tlen = FLINT_MIN(2 * m - 1, n);
        ulen = FLINT_MIN(n, m + tlen - 1);

        status |= _gr_poly_mullow(t, g, m, g, m, tlen, ctx);
        status |= _gr_poly_mullow(u, g, m, t, tlen, ulen, ctx);

        if (have_mulmid)
        {
            status |= _gr_poly_mulmid(GR_ENTRY(g, m, sz), u, ulen, h, FLINT_MIN(hlen, n), m, n, ctx);
            status |= _gr_vec_mul_scalar_2exp_si(GR_ENTRY(g, m, sz), GR_ENTRY(g, m, sz), n - m, -1, ctx);
        }
        else
        {
            status |= _gr_poly_mullow(t, u, ulen, h, FLINT_MIN(hlen, n), n, ctx);
            status |= _gr_vec_mul_scalar_2exp_si(GR_ENTRY(g, m, sz), GR_ENTRY(t, m, sz), n - m, -1, ctx);
        }

        status |= _gr_vec_neg(GR_ENTRY(g, m, sz), GR_ENTRY(g, m, sz), n - m, ctx);
    }

    m = (len + 1) / 2;
    n = len;

    /* Karp-Markstein */
    /* todo: cleanup; improve allocations? */
    tlen = FLINT_MIN(2 * m - 1, n);
    status |= _gr_poly_mullow(v, g, m, h, hlen, m, ctx);

    if (have_mulmid)
    {
        if (m < tlen)
            status |= _gr_poly_mulmid(t, v, m, v, m, m, tlen, ctx);
        status |= _gr_poly_sub(GR_ENTRY(u, m, sz), GR_ENTRY(h, m, sz),
            FLINT_MAX(0, FLINT_MIN(hlen - m, n - m)), t, FLINT_MAX(0, FLINT_MIN(tlen - m, n - m)), ctx);
    }
    else
    {
        status |= _gr_poly_mullow(t, v, m, v, m, tlen, ctx);
        status |= _gr_poly_sub(GR_ENTRY(u, m, sz), GR_ENTRY(h, m, sz),
            FLINT_MAX(0, FLINT_MIN(hlen - m, n - m)), GR_ENTRY(t, m, sz), FLINT_MAX(0, FLINT_MIN(tlen - m, n - m)), ctx);
    }

    status |= _gr_poly_mullow(GR_ENTRY(g, m, sz), g, m, GR_ENTRY(u, m, sz), n - m, n - m, ctx);
    status |= _gr_vec_mul_scalar_2exp_si(GR_ENTRY(g, m, sz), GR_ENTRY(g, m, sz), n - m, -1, ctx);
    _gr_vec_swap(g, v, m, ctx);

    GR_TMP_CLEAR_VEC(t, alloc, ctx);

    return status;
}

int
gr_poly_sqrt_series_newton(gr_poly_t res, const gr_poly_t h, slong len, slong cutoff, gr_ctx_t ctx)
{
    int status = GR_SUCCESS;
    slong hlen;

    hlen = h->length;

    if (hlen == 0 || len == 0)
        return gr_poly_zero(res, ctx);

    if (hlen == 1)
        len = 1;

    if (res == h)
    {
        gr_poly_t t;
        gr_poly_init(t, ctx);
        status = gr_poly_sqrt_series_newton(t, h, len, cutoff, ctx);
        gr_poly_swap(res, t, ctx);
        gr_poly_clear(t, ctx);
        return status;
    }

    gr_poly_fit_length(res, len, ctx);
    status |= _gr_poly_sqrt_series_newton(res->coeffs, h->coeffs, h->length, len, cutoff, ctx);
    _gr_poly_set_length(res, len, ctx);
    _gr_poly_normalise(res, ctx);
    return status;
}